According to GAAP is it acceptable to record an invoice payment in the month it is paid vs the month it is received?

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This isn't a homework question just tryng to interpret correct way to post

In GAAP costs should be recorded in the period (month) that the cost was incurred, regardless of when the invoice is received or the cash paid.

However, if you have a small business (like a sole proprietorship) it is acceptable not to follow GAAP and use cash accounting and therefore only recognize expenses when they are paid.

Does that clear it up for you?